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 Post subject: Can I factor this?Posted: Sun, 15 Jul 2012 20:22:44 UTC
 S.O.S. Oldtimer

Joined: Tue, 27 Jul 2004 05:19:28 UTC
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Location: Houston, Texas
(1-x)^(gM/RL)

To

(1-x)^((gM/RL)-1)

Is this mathmatically correct?

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 Post subject: Re: Can I factor this?Posted: Sun, 15 Jul 2012 23:35:40 UTC
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Joined: Mon, 19 May 2003 19:55:19 UTC
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Hello, ShawnGroskreutz!

Quote:

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 Post subject: Re: Can I factor this?Posted: Mon, 16 Jul 2012 00:46:14 UTC
 S.O.S. Oldtimer

Joined: Tue, 27 Jul 2004 05:19:28 UTC
Posts: 161
Location: Houston, Texas
Soroban,
Are you familiar with the Dervivation of the equation for Density Altitude based upon the three following
Equations from our 1976 standard atmosphere.

T=To-L*H

P=Po[1-(L*H/To)]^(g*M/R*L)

D=[P*M]/R*T*1000

I have had a very difficult time getting the correct equation: Which is

H=(To/L)[1-[(1000RToD/M*Po)]^[(L*R/g*M-L*R)]

I have been trying to get the derivation all day to no avail. Could you show a detailed derivation including how to get the exponential factor correct.

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 Post subject: Re: Can I factor this?Posted: Mon, 16 Jul 2012 02:56:44 UTC
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That doesn't make any difference, you cannot subtract a power and expect it to be the same thing.

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 Post subject: Re: Can I factor this?Posted: Mon, 16 Jul 2012 09:47:29 UTC
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You have confused the density altitude with the pressure altitude . The formula for is exactly the same as for except that the exponent is one less.

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 Post subject: Re: Can I factor this?Posted: Mon, 16 Jul 2012 13:37:17 UTC
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Shawn, go stand in the corner and repent

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 Post subject: Re: Can I factor this?Posted: Mon, 16 Jul 2012 15:50:37 UTC
 S.O.S. Oldtimer

Joined: Tue, 27 Jul 2004 05:19:28 UTC
Posts: 161
Location: Houston, Texas

At this point, the only difference between my result and the correct result is the exponential term. The correct equation is:

So, this is where I am stuck.

The three original equations were:

T = To -L*H

P = Po(1-(L*H/To))^[g*M/R*L}

D = P*M/R*T*1000

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 Post subject: Re: Can I factor this?Posted: Mon, 16 Jul 2012 16:09:27 UTC
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Substituting the first two equations into the third,

and rearranging gives

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 Post subject: Re: Can I factor this?Posted: Mon, 16 Jul 2012 17:42:09 UTC
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Joined: Tue, 27 Jul 2004 05:19:28 UTC
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Location: Houston, Texas
That is it. Thank-you.

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 Post subject: Re: Can I factor this?Posted: Tue, 17 Jul 2012 17:34:56 UTC
 S.O.S. Oldtimer

Joined: Tue, 27 Jul 2004 05:19:28 UTC
Posts: 161
Location: Houston, Texas
[/quote]

Hey, I need help evaluation the units of that particular equation. It seems to me that they don't all evaluate out to Kilometers.

Anyway:

To = 288.15 degrees kelvin
L = 6.5 degrees kelvin/KM
R = 8.31432 J/Mol degree K
g = 9.8065 m/sec^2
M = 28.9644 g/mol

Could someone show that the units all cancel out to Kilometers. I tried to evaluate the units and I am not getting a good result.

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 Post subject: Re: Can I factor this?Posted: Wed, 18 Jul 2012 04:56:37 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Location: Austin, TX
ShawnGroskreutz wrote:

Hey, I need help evaluation the units of that particular equation. It seems to me that they don't all evaluate out to Kilometers.

Anyway:

To = 288.15 degrees kelvin
L = 6.5 degrees kelvin/KM
R = 8.31432 J/Mol degree K
g = 9.8065 m/sec^2
M = 28.9644 g/mol

Could someone show that the units all cancel out to Kilometers. I tried to evaluate the units and I am not getting a good result.[/quote]

Just check that gives km, the others are all pure numbers.

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 Post subject: Re: Can I factor this?Posted: Wed, 18 Jul 2012 16:05:08 UTC
 S.O.S. Oldtimer

Joined: Tue, 27 Jul 2004 05:19:28 UTC
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Thanks, after knashing teeth for a while, I was able to prove that every unit cancels out, except for Km, and the rest of the equation is dimensionless.

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 Post subject: Re: Can I factor this?Posted: Wed, 18 Jul 2012 18:50:21 UTC
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ShawnGroskreutz wrote:
Thanks, after knashing teeth for a while, I was able to prove that every unit cancels out, except for Km, and the rest of the equation is dimensionless.

I think you mean "gnashing", and I'm glad you figured it out.

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